Given $ m \angle ABC = 2x + 154$, and $ m \angle CBD = 2x + 22$, find $m\angle CBD$. $B$ $A$ $D$ $C$
From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 154} + {2x + 22} = {180}$ Combine like terms: $ 4x + 176 = 180$ Subtract $176$ from both sides: $ 4x = 4$ Divide both sides by $4$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 2({1}) + 22$ Simplify: $ {m\angle CBD = 2 + 22}$ So ${m\angle CBD = 24}$.